Livingston, who finished with 20 points and 10 boards, chased down a rebound after Josh Hagins missed a jump shot with 39 seconds left, and the Red Wolves held on to give Arkansas-Little Rock its first loss in Sun Belt Conference action.
Arkansas-Little Rock's Marcus Johnson Jr. got off a 3-point attempt as time expired, but it bounced off the rim.
The Arkansas State win gave coach John Brady his 400th career victory.
Trailing 48-30 at the half, the Trojans charged back and closed to 74-73 with 1:16 left.
Hagins scored 12 of his 16 points in the second half. Roger Woods also had 16 for Arkansas-Little Rock (15-2, 5-1).